If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. (Round Mean, Standard Deviation, z-value to 2 decimal places and Probability to 4 decimal places.) Path Mean Std. Dev. a-d-e-h 24.33 1.35 a-f-g 15.50 1.26 b-i-j-k 14.83 1.02 c-m-n-o 26.17 1.66 Probability ($1,000) .4099

(a) Probability of $1,000 bonus = 0.4099

(b) Probability of $500 bonus = 0.6742

1. path a-d-e-h

Mean = 24.33      Standard Deviation = 1.35         z-value = 1.23  

2. Path a-f-g

Mean =  15.50    Standard Deviation = 1.26  z-value =   8.35

3. Path  b-i-j-k

Mean = 14.83      Standard Deviation =  1.02 z-value =  11.02

4. Path c-m-n-o

Mean =  26.17   Standard Deviation = 1.66  z-value =  -0.10

Step-by-step explanation:

See the attached for the calculations

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.